(2) A siphon tube with vertical arms filled with mercury, and closed at both ends is inserted into a σ, basin of water. of S.G. When the stoppers are removed, examine what will ensue, and prove the following results if the barometer is sufficiently high : (1) If b, the whole length of the outside arm, exceeds a, the whole length of the immersed arm, the mercury will flow outwards and the water will follow it. (2) If ab, the end of the immersed tube must be at a depth below the free surface of the water exceeding (a - b)σ in order that the mercury may not flow back into the basin. (3) Two equal cylinders side by side contain mercury, one quite full and open at the top, the other full to 20 inches from the top and closed, the 20 inches being occupied by air at the atmospheric pressure, which is 30 inches of the barometric column. If the two vessels are connected by a siphon dipping into the two liquids, prove that, when the siphon is put in action, 5 inches of mercury will flow from one of the cylinders into the other. What takes place when the leg of the siphon which is in the closed cylinder is not long enough to reach the mercury in that cylinder? CHAPTER VII. PNEUMATICS. THE GASEOUS LAWS. 196. Hitherto we have dealt with the properties of Liquids or Incompressible Fluids like Water; and now we proceed to consider Air and Gases, or Compressible Fluids, and their properties, a branch of Hydrostatics sometimes called Pneumatics, from the Greek word πvevματική, meaning the science which concerns πνεῦμα, εν or gas. A given quantity of a Gas (“a parcel of gas" in Boyle's words) requires to be kept in a closed vessel, to prevent diffusion; and by changing the volume of the vessel and the temperature, the pressure of the gas is altered. Given the volume and the temperature, the pressure of a given quantity of a gas is determinate; so that the pressure p is a function of the volume v or density p, and of the temperature 7. or Expressed analytically p=f(v, 7), F(p, v, t) = 0 ; and to determine this function, two new Laws, based upon experiment, are required, which are called 280 THE GASEOUS LAWS 197. The Gaseous Laws. LAW I-BOYLE'S LAW. "At constant temperature the pressure of a given quantity of a Gas is inversely proportional to the volume, or directly to the density." This law was enunciated by Boyle in his Defence of the Doctrine touching the Spring and Weight of the Air in answer to Linus, 1662; abroad it is attributed to Mariotte, who did not however publish it till 1676. Thus if p denotes the pressure and v the volume of unit quantity of the gas, one gramme suppose, and denotes the density, so that p=1/v, then p=kp, or pv=k, ρ where k depends only on the temperature: so that, on the (p, v) diagram, an isothermal is a hyperbola (fig. 65), along which the hydrostatic energy pv (§ 14) is constant. For instance, a guuner, who can push with a force of P pounds, can, under an atmospheric pressure of p lb/in2, introduce an airtight sponge into a closed cannon, dins in calibre and 7 ins long in the bore, a distance x ins, given by P l=120, we find that LAW II-CHARLES'S OR GAY-LUSSAC'S LAW. "At constant pressure the volume of the Gas increases uniformly with the temperature, and at the same rate for Combining this with Boyle's Law we find that the product of the pressure and volume of a given quantity of OF BOYLE AND CHARLES. 281 any Gas increases uniformly with the temperature at the same rate; so that we may write pv=k=k(1+aT), where a is a constant coefficient of expansion, the same for all gases. On the Centigrade scale of temperature and now putting a=0·003665=273; k=R/a (the height of the homogenous atmosphere at 0 C). and is called the absolute temperature, and — 1/a the absolute zero; this is therefore -273 C, or about - 460 F, since 1/a = x 273-492 on the Fahrenheit scale. But 274 C, or -461 F is sometimes taken as nearer to the correct value of the absolute zero of temperature. At this absolute zero the pressure of a given quantity of gas would be zero, whatever the volume. In an experiment by Robins (New Principles of Gunnery, Prop. V., p. 70) a gun barrel, which would contain about 800 grains of water, was raised to a white heat, and plunged into water, when it was found that about 600 grains of water had entered the barrel. This proves that the air left in the barrel had been expanded to four times its volume; so that, if the water was at 15° C, or 288 absolute, the temperature of the white heat was about 1152 absolute, or 880° C, or 1552° F. 198. The equation = ..... .(A) connecting p the pressure, v the volume, and the absolute temperature of a given quantity, say one g, is called the Characteristic Equation of a Perfect Gas. 282 THE CHARACTERISTIC SURFACE. It may be illustrated geometrically by the surface shown in fig. 65, in which the isothermals, along which O is constant, are hyperbolas, while the isometrics, v constant, and the isobars, p constant, are straight lines. This model surface can be constructed of pieces of cardboard, as made by Brill of Darmstadt. Denoting by P, V, ✪ the pressure volume, and temperature in any given initial state, then (A) may be written pv PV = Ꮎ Ꮎ R= = embodying the Laws of Boyle and Charles in a form suitable for calculation from experiments. Regnault found that at Paris a litre of dry air at 0 C and a barometric height 76 cm is 1-293187 g; so that measuring pressure in millimetres of mercury head, we find, for a gramme of air at Paris, and P=760, p=1/V=001293187, 0=273, R=PV/O=215.3. Taking the density of mercury as 13:59, this makes the height at Paris of the homogeneous atmosphere at 0 C k=ho/p=798676.5 cm, say 8000 m. The weight in g of V litres of dry air at a temperature C and a pressure of h mm of mercury is therefore a formula required in exact weighings, in allowing for the buoyancy of the air. 199. It must be noticed that the gravitation measure of force is employed in these formulas, so that in accurate comparisons the local value of g must be allowed for. Thus if g changes to g' in going from Paris to any other locality, Greenwich for instance, the absolute pres |